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| author | Ian Jauslin <ian@jauslin.org> | 2020-12-16 22:41:24 +0100 |
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| committer | Ian Jauslin <ian@jauslin.org> | 2020-12-16 22:41:24 +0100 |
| commit | 1038647506b9d897e73bf465a381f03aab6fb19e (patch) | |
| tree | c61377e7ae51eab164c97b357ab76443c4d16852 | |
38 files changed, 2406 insertions, 0 deletions
diff --git a/Jauslin_Rutgers_2020.tex b/Jauslin_Rutgers_2020.tex new file mode 100644 index 0000000..ba898a6 --- /dev/null +++ b/Jauslin_Rutgers_2020.tex @@ -0,0 +1,398 @@ +\documentclass{ian-presentation} + +\usepackage[hidelinks]{hyperref} +\usepackage{graphicx} +\usepackage{array} +\usepackage{xcolor} + + +\definecolor{ipurple}{HTML}{4B0082} +\definecolor{iyellow}{HTML}{DAA520} +\definecolor{igreen}{HTML}{32CD32} +\definecolor{iblue}{HTML}{4169E1} +\definecolor{ired}{HTML}{DC143C} + +\definecolor{highlight}{HTML}{328932} +\definecolor{highlight}{HTML}{981414} + +\begin{document} +\pagestyle{empty} +\hbox{}\vfil +\bf\Large +\hfil Analysis of a non-linear, non-local PDE\par +\hfil to study Bose gases at all densities +\vfil +\large +\hfil Ian Jauslin +\normalsize +\vfil +\rm +\hfil collaborators: {\bf E.A.\-~Carlen, E.H.\-~Lieb, M.\-~Holzmann, M.P.\-~Loss}\par +\vfil +arXiv:{\tt\ \parbox[b]{3cm}{ + \href{https://arxiv.org/abs/1912.04987}{1912.04987}\par + \href{https://arxiv.org/abs/2010.13882}{2010.13882}\par + \href{https://arxiv.org/abs/2011.10869}{2011.10869} +}} +\hfill{\tt \href{http://ian.jauslin.org}{http://ian.jauslin.org}} +\eject + +\setcounter{page}1 +\pagestyle{plain} + +\title{{\color{iblue}Simple equation}} +\begin{itemize} + \item {\color{iblue}Simple equation} + $$ + -\Delta u(x)=(1-u(x))v(x)- 4eu(x)+2e\rho\ u\ast u(x) + $$ + $$ + e=\frac\rho2\int dx\ (1-u(x))v(x) + $$ + \item $\rho>0$, $v(x)\geqslant 0$, $v\in L_1(\mathbb R^3)$. + \item {\color{highlight}Non-linear} and {\color{highlight}non-local} partial differential equation. + \item {\color{highlight}Effective equation} for the ground state of a Bose gas. +\end{itemize} +\vfill +\eject + +\title{Bose-Einstein condensation} +\begin{itemize} +\item System of many Bosons, e.g. {\color{highlight}Helium} atoms, {\color{highlight}Rubidium} atoms, etc... +\item {\color{highlight}Bose-Einstein condensate}: most particles are in the same quantum state. +\item Related to the phenomena of {\color{highlight}superfluidity} (flow with zero viscocity) and {\color{highlight}superconductivity} (currents with zero resistance). +\item Predicted theoretically in {\color{highlight}1924-1925}, experimentally observed in {\color{highlight}1995}. +\item Mathematical understanding: still {\color{highlight}no proof} of the existence of a condensate (at finite density, in the presence of interactions and in the continuum). +\end{itemize} +\vfill +\eject + +\title{Repulsive Bose gas} +\begin{itemize} + \item {\color{highlight}$N$-particle} quantum state in a volume $V$: + $$ + \psi_N(x_1,\cdots,x_N)\in L^2_{\mathrm{symmetric}}((V\mathbb T^3)^N) + $$ + + \item $|\psi|^2$: probability distribution on the positions of the $N$ particles. + + \item Hamiltonian operator acting on $\psi$: + $$ + H_N\psi:= + -\frac12\sum_{i=1}^N\Delta_i\psi + +\sum_{1\leqslant i<j\leqslant N}{\color{highlight}v(|x_i-x_j|)}\psi + $$ + {\color{highlight}$v(r)\geqslant 0$}, {\color{highlight}$\hat v(k)\geqslant 0$} and {\color{highlight}$v\in L_1(\mathbb R^3)$}. +\vfill +\eject + +\title{Energy and condensate fraction} +\vskip-10pt + \item Ground state: $\psi_0$, energy $E_0$: + $$ + H_N\psi_0={\color{highlight}E_0}\psi_0 + $$ +\vskip-10pt + \item In the {\color{highlight}thermodynamic limit}: + $$ + e_0:=\lim_{\displaystyle\mathop{\scriptstyle V,N\to\infty}_{{\color{highlight}\frac NV=\rho}}}\frac{E_0}N + . + $$ +\vskip-5pt + \item Condensate fraction: proportion of particles in the Bose-Einstein condensate: in the {\color{highlight}thermodynamic limit}: + $$ + \eta_0:=\lim_{\displaystyle\mathop{\scriptstyle V,N\to\infty}_{{\color{highlight}\frac NV=\rho}}}\frac1N\left<\psi_0\right|\sum_{i=1}^N\int\frac{dx_i}V\left|\psi_0\right> + . + $$ +\end{itemize} +\vfill +\eject + +\title{Low density conjectures} +\begin{itemize} + \item Bogolyubov theory: {\color{highlight}approximation scheme} [Bogolyubov, 1947]. + \item Predictions \href{https://doi.org/10.1103/PhysRev.106.1135}{[Lee, Huang, Yang, 1957]}: + \begin{itemize} + \item Energy: + $$ + {\color{highlight}e_0=2\pi\rho a\left(1+\frac{128}{15\sqrt\pi}\sqrt{\rho a^3}+o(\sqrt\rho)\right)} + $$ + \vskip-10pt + \item Condensate fraction: + $$ + {\color{highlight}1-\eta_0\sim\frac{8\sqrt{\rho a^3}}{3\sqrt\pi}} + $$ + \end{itemize} +\end{itemize} +\vfill +\eject + +\title{Low density conjectures} +\begin{itemize} + \item Energy asymptotics: {\color{highlight} proved}: + \href{https://doi.org/10.1103/PhysRevLett.80.2504}{[Lieb, Yngvason, 1998]}, + \href{https://doi.org/10.1007/s10955-009-9792-3}{[Yau, Yin, 2009]}, + \href{https://doi.org/10.4007/annals.2020.192.3.5}{[Fournais, Solovej, 2020]}. + + \item Condensate fraction: {\color{highlight}still open} in the thermodynamic limit. (No proof of Bose-Einstein condensation.) + + \item There are proofs of condensation in the ultra-dilute (Gross-Pitaevskii) regime: + \href{https://doi.org/10.1103/PhysRevLett.88.170409}{[Lieb, Seiringer, 2002]}, + \href{https://doi.org/10.1007/s00220-017-3016-5}{[Boccato, Brennecke, Cenatiempo, Schlein, 2018]}. + + \item There is also a proof of condensation for a {\color{highlight}lattice} Bose gas + \href{https://doi.org/10.1007/BF01023854}{[Kennedy, Lieb, Shastry, 1988]}. +\end{itemize} +\vfill +\eject + +\title{High density conjectures} +\begin{itemize} + \item [Bogolyubov, 1947]: + $$ + {\color{highlight}e_0\sim\frac\rho2\int v} + $$ + \item {\color{highlight}Proved} in \href{https://doi.org/10.1103/PhysRev.130.2518}{[Lieb, 1963]}. + + \item Condensate fraction: mean field regime: $\eta_0\to 1$. (No proof of Bose-Einstein condensation at any density.) +\end{itemize} +\vfill +\eject + +\title{Energy as a function of density for the {\color{iblue}Simple equation}} +For $v(x)=e^{-|x|}$: + +\hfil\includegraphics[height=5.5cm]{erho_lowhigh.pdf} +\vfill +\eject + +\addtocounter{page}{-1} +\title{Energy as a function of density for the {\color{iblue}Simple equation}} +For $v(x)=e^{-|x|}$: + +\hfil\includegraphics[height=5.5cm]{erho_effective.pdf} +\vfill +\eject + +\title{Effective equations} +\begin{itemize} + \item {\color{highlight}Boltzmann equation}: $N$ classical hard particles with an infinitely small radius (dilute limit) + [Lanford, 1976]. + \item {\color{highlight}Thomas-Fermi theory}: $Z$ electrons orbiting a nucleus in the $Z\to\infty$ limit + \href{https://doi.org/10.1103/PhysRevLett.31.681}{[Lieb, Simon, 1973]}. + \item{\color{highlight}Hartree-Fock equation}: dynamics of many Fermions in the weakly-interacting limit + \href{https://doi.org/10.1142/9789814618144_0011}{[Benedikter, Porta, Schlein, 2015]}. + \item{\color{highlight}Hartree-Fock-Bogolyubov equation}: dynamics of many Bosons in the weakly-interacting limit + \href{https://arxiv.org/abs/1602.05171}{[Bach, Breteaux, Chen, Fr\"ohlich, Sigal, 2016]}. +\end{itemize} +\vfill +\eject + +\title{Derivation of the equation} +\begin{itemize} + \item \href{https://doi.org/10.1103/PhysRev.130.2518}{[Lieb, 1963]}. + \item Integrate $H_N\psi_0=E_0\psi_0$: + $$ + \int dx_1\cdots dx_N\ + \left( + -\frac12\sum_{i=1}^N\Delta_i\psi_0 + +\sum_{1\leqslant i<j\leqslant N} v(x_i-x_j)\psi_0 + \right) + =E_0\int dx_1\cdots dx_N\ \psi_0 + $$ + \item Therefore, + $$ + \frac{N(N-1)}2\int dx_1dx_2\ v(x_1-x_2)\frac{\int dx_3\cdots dx_N\ \psi_0}{\int dx_1\cdots dx_N\ \psi_0} + =E_0 + $$ +\end{itemize} +\vfill +\eject + +\title{Derivation of the equation} +\begin{itemize} + \item Thus, + $$ + \frac{E_0}N=\frac{N-1}{2V}\int dx\ v(x)g_2(0,x) + $$ + \item {\color{highlight}$\psi_0\geqslant 0$}, so it can be thought of as a probability distribution. + \item $g_n$: {\color{highlight}correlation functions} of $\psi_0$ + $$ + g_n(x_1,\cdots,x_n):=\frac{V^n\int dx_{n+1}\cdots dx_N\ \psi_0(x_1,\cdots,x_N)}{\int dx_1\cdots dx_N\ \psi_0(x_1,\cdots,x_N)} + $$ +\end{itemize} +\vfill +\eject + +\title{Hierarchy} +\vskip-10pt +\begin{itemize} + \item Equation for $g_2$: integrate $H_N\psi_0=E_0\psi_0$ with respect to $x_3,\cdots,x_N$: + $$ + \begin{array}{>\displaystyle l} + -\frac12(\Delta_x+\Delta_y) g_2(x,y) + +\frac{N-2}V\int dz\ (v(x-z)+v(y-z))g_3(x,y,z) + \\[0.5cm]\hfill + +v(x-y)g_2(x,y) + +\frac{(N-2)(N-3)}{2V^2}\int dzdt\ v(z-t)g_4(x,y,z,t) + =E_0g_2(x,y) + \end{array} + $$ + \item Factorization {\color{highlight}assumption}: + $$ + g_3(x_1,x_2,x_3)=g_2(x_1,x_2)g_2(x_1,x_3)g_2(x_2,x_3) + $$ + $$ + g_4(x_1,x_2,x_3,x_4)=\prod_{i<j}(g_2(x_i,x_j)+O(V^{-1})) + $$ +\end{itemize} +\vfill +\eject + +\title{{\color{ipurple}Big equation}} +\begin{itemize} +\item In the thermodynamic limit, if ${\color{highlight}u(x):=1-g_2(0,x)}$, + $$ + -\Delta u(x) + = + (1-u(x))\left(v(x)-2\rho K(x)+\rho^2 L(x)\right) + $$ + $$ + K:= + u\ast S + ,\quad + S(y):=(1-u(y))v(y) + $$ + $$ + L:= + u\ast u\ast S + -2u\ast(u(u\ast S)) + +\frac12 + \int dydz\ u(y)u(z-x)u(z)u(y-x)S(z-y) + . + $$ + + \item {\color{ipurple}``Big'' equation}: + $$ + L\approx + u\ast u\ast S. + $$ +\end{itemize} +\vfill +\eject + +\title{{\color{iblue}Simple equation}} +\vskip-10pt +\begin{itemize} + \item Further approximate $S(x)\approx\frac{2e}\rho\delta(x)$ and $u\ll 1$. + \item Simple equation + $$ + {\color{iblue}-\Delta u(x)=(1-u(x))v(x)- 4eu(x)+2e\rho\ u\ast u(x)} + $$ + $$ + {\color{iblue}e=\frac\rho2\int dx\ (1-u(x))v(x)} + $$ + \item {\bf Theorem 1}: + If $v(x)\geqslant 0$ and $v\in L_1\cap L_2(\mathbb R^3)$, then the {\color{iblue}simple equation} has an {\color{highlight}integrable solution} (proved constructively), with $0\leqslant u\leqslant 1$. +\end{itemize} +\vfill +\eject + +\title{Energy for the {\color{iblue}simple equation}} +\vskip-10pt +\begin{itemize} + \item {\bf Theorem 2}: + $$ + \frac{e}{\rho}\mathop{\longrightarrow}_{\rho\to\infty}\frac12\int dx\ v(x) + . + $$ + This coincides with the {\color{highlight}Hartree energy}. + \item {\bf Theorem 3}: + $$ + e=2\pi\rho a\left(1+\frac{128}{15\sqrt\pi}\sqrt{\rho a^3}+o(\sqrt\rho)\right) + $$ + This coincides with the {\color{highlight}Lee-Huang-Yang prediction}. +\end{itemize} +\vfill +\eject + +\title{Energy} +$v(x)=e^{-|x|}$, Blue: {\color{iblue}simple equation}; purple: {\color{ipurple}big equation}; red: {\color{ired}Monte Carlo} + +\hfil\includegraphics[height=5.5cm]{erho_fulleq.pdf} +\vfill +\eject + +\title{Condensate fraction} +\begin{itemize} + \item Add a parameter $\mu$ to the Hamiltonian: + $$ + H_N(\mu):= + -\frac12\sum_{i=1}^N\Delta_i + +\sum_{1\leqslant i<j\leqslant N}v(x_i-x_j) + {\color{highlight}-\mu\sum_{i=1}^N\int\frac{dx_i}V\ \cdot} + $$ + \item Projection onto condensate wavefunction: $\sum_i\int\frac{dx_i}V$. + \item Condensate fraction: + $$ + {\color{highlight}\eta_0}:=\frac1N\left<\psi_0\right|\sum_{i=1}^N\int\frac{dx_i}V\left|\psi_0\right> + =-\frac1N\partial_\mu \left<\psi_0\right|H_N(\mu)\left|\psi_0\right>|_{\mu_0} + \equiv + {\color{highlight}-\partial_\mu e_0(\mu)|_{\mu=0}} + $$ +\end{itemize} +\vfill +\eject + +\title{Condensate fraction} +\begin{itemize} + \item {\bf Theorem 4}: + For the {\color{iblue}simple equation}, as $\rho\to0$ + $$ + 1-\eta\sim\frac{8\sqrt{\rho a^3}}{3\sqrt\pi} + $$ + which coincides with {\color{highlight}Bogolyubov's prediction}. + + \item In particular {\color{highlight}there is Bose-Einstein condensation} for the simple equation. +\end{itemize} +\vfill +\eject + +\title{Condensate fraction} +$v(x)=e^{-|x|}$, Blue: {\color{iblue}simple equation}; purple: {\color{ipurple}big equation}; red: {\color{ired}Monte Carlo} + +\hfil\includegraphics[height=5.5cm]{condensate.pdf} +\vfill +\eject + +\title{Conclusions and outlook} +\begin{itemize} + \item Two {\color{highlight}effective equations}: the {\color{ipurple}big equation} and the {\color{iblue}simple equation}, which are {\color{highlight}non-linear 1-particle equations}. + \item Reproduce the known results for both {\color{highlight}small and large densities}. + \item Their derivation is {\color{highlight}different from Bogolyubov theory}, so they may give new insights onto studying the Bose gas in these asymptotic regimes. + \item The {\color{ipurple}big equation} is {\color{highlight}quantitatively accurate} at intermediate densities. + \item This opens up the possibility of studying the physics of the {\color{highlight}Bose gas at intermediate densities}. +\end{itemize} +\vfill +\eject + +\title{Open problems and next steps} +\vskip-10pt +\begin{itemize} + \item Analysis of the {\color{ipurple}big equation}: everything is still open. +\vskip-10pt + \begin{itemize} + \item Main tool: {\color{highlight}Newton algorithm}, which works numerically. + \item There is a family of {\color{highlight}intermediate equations} that extrapolate between the {\color{iblue} simple} and {\color{ipurple}big} equations. + \end{itemize} + + \item Relate these equations back to the {\color{highlight}many-body Bose gas}. + \vskip-10pt + \begin{itemize} + \item {\color{highlight}Upper bound} for the ground state energy, using a {\color{highlight}Bijl function} as a test function. + \item {\color{highlight}Lee-Huang Yang formula} by studying the low-density properties of the {\color{highlight}Bijl function}. + \item Extend the proof to the {\color{highlight}condensate fraction}. + \end{itemize} +\end{itemize} + +\end{document} diff --git a/Makefile b/Makefile new file mode 100644 index 0000000..d32a79c --- /dev/null +++ b/Makefile @@ -0,0 +1,50 @@ +PROJECTNAME=$(basename $(wildcard *.tex)) +LIBS=$(notdir $(wildcard libs/*)) +FIGS=$(notdir $(wildcard figs/*.fig)) +JPGS=$(notdir $(wildcard figs/*.jpg)) + +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) +SYNCTEXS=$(addsuffix .synctex.gz, $(PROJECTNAME)) + +all: $(PROJECTNAME) + +$(PROJECTNAME): $(LIBS) $(FIGS) $(JPGS) + pdflatex -file-line-error $@.tex + pdflatex -synctex=1 $@.tex + +$(SYNCTEXS): $(LIBS) $(FIGS) $(JPGS) + pdflatex -synctex=1 $(patsubst %.synctex.gz, %.tex, $@) + + +$(LIBS): + ln -fs libs/$@ ./ + + +$(FIGS): + make -C figs/$@ + for pdf in $$(find figs/$@/ -name '*.pdf'); do ln -fs "$$pdf" ./ ; done + +$(JPGS): + ln -fs figs/$@ ./ + + +clean-aux: clean-figs-aux + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + rm -f $(addsuffix .out, $(PROJECTNAME)) + +clean-libs: + rm -f $(LIBS) + +clean-figs: + $(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean; ) + rm -f $(notdir $(wildcard figs/*.fig/*.pdf)) + +clean-figs-aux: + $(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean-aux; ) + + +clean-tex: + rm -f $(PDFS) $(SYNCTEXS) + +clean: clean-aux clean-tex clean-libs clean-figs @@ -0,0 +1,33 @@ +This directory contains the source files to typeset the presentation, and +generate the figures. This can be accomplished by running + make + +This document uses a custom class file, located in the 'libs' directory, which +defines a number of commands. + + +* Dependencies: + + pdflatex + TeXlive packages: + amsfonts + array + graphics + hyperref + latex + pgf + standalone + GNU make + gnuplot + +* Files: + + Jauslin_Rutgers_2020.tex: + main LaTeX file + + libs: + custom LaTeX class file + + figs: + source code for the figures + diff --git a/figs/condensate.fig/Makefile b/figs/condensate.fig/Makefile new file mode 100644 index 0000000..c45de65 --- /dev/null +++ b/figs/condensate.fig/Makefile @@ -0,0 +1,34 @@ +PROJECTNAME=condensate + +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) +DATS= simpleq.dat bigeq.dat + +all: $(PDFS) + +$(PDFS): $(DATS) + gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@) + pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@) + +simpleq.dat: + julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=1" -M simpleq condensate_fraction > $@ +bigeq.dat: + julia -p 8 $(SIMPLEQ)/main.jl -p "eq=bigeq;N=12;P=8;v_a=1" -M medeq condensate_fraction > $@ + +install: $(PDFS) + cp $^ $(INSTALLDIR)/ + +$(LIBS): + ln -fs libs/$@ ./ + +clean-libs: + rm -f $(LIBS) + +clean-aux: + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + rm -f $(addsuffix .tex, $(PROJECTNAME)) + +clean-tex: + rm -f $(PDFS) + +clean: clean-libs clean-aux clean-tex diff --git a/figs/condensate.fig/bigeq.dat b/figs/condensate.fig/bigeq.dat new file mode 100644 index 0000000..e48cbc3 --- /dev/null +++ b/figs/condensate.fig/bigeq.dat @@ -0,0 +1,100 @@ + 1.000000000000000e-06 1.942109602248065e-03 1.702970665674168e-12 + 1.202264434617413e-06 2.144142093189251e-03 1.178808810520995e-13 + 1.445439770745928e-06 2.370859341242408e-03 1.192336354552407e-12 + 1.737800828749376e-06 2.623985546948715e-03 4.076932518598860e-12 + 2.089296130854041e-06 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8.712493630911380e-02 4.144857506288649e-15 + 8.317637711026709e-03 8.931723938183408e-02 3.530020645632524e-15 + 1.000000000000000e-02 9.115971178417075e-02 6.924046664381005e-15 + 1.202264434617413e-02 9.262971027971965e-02 6.034088541831901e-15 + 1.445439770745928e-02 9.371241367329312e-02 4.885148310946663e-15 + 1.737800828749376e-02 9.440112413816591e-02 2.917320379507791e-15 + 2.089296130854041e-02 9.469715660989715e-02 2.610686638602541e-15 + 2.511886431509582e-02 9.460934902764143e-02 7.354666705237897e-15 + 3.019951720402019e-02 9.415325731511556e-02 5.796225767460134e-15 + 3.630780547701010e-02 9.335011969104240e-02 6.017084081620531e-15 + 4.365158322401656e-02 9.222568368303644e-02 5.302998003473651e-15 + 5.248074602497723e-02 9.080898675648411e-02 4.039838886119182e-15 + 6.309573444801930e-02 8.913117007641815e-02 4.125816885656187e-15 + 7.585775750291836e-02 8.722438779915097e-02 4.273284938741890e-15 + 9.120108393559097e-02 8.512085476424038e-02 2.623094380645173e-15 + 1.096478196143185e-01 8.285205637207869e-02 4.927649012520671e-15 + 1.318256738556407e-01 8.044812781958981e-02 2.420044464772237e-15 + 1.584893192461114e-01 7.793739685903543e-02 2.149025610829404e-15 + 1.905460717963248e-01 7.534607518083469e-02 3.388825035919124e-15 + 2.290867652767775e-01 7.269807815050612e-02 2.822970856541473e-15 + 2.754228703338169e-01 7.001495034676258e-02 4.182630891668936e-15 + 3.311311214825908e-01 6.731587439715549e-02 2.904212967331170e-15 + 3.981071705534969e-01 6.461774223707760e-02 5.477274398838064e-15 + 4.786300923226380e-01 6.193527047174405e-02 4.783552039455272e-15 + 5.754399373371566e-01 5.928114448311252e-02 4.439456789833779e-15 + 6.918309709189363e-01 5.666617892504009e-02 3.191356061395679e-15 + 8.317637711026709e-01 5.409948505148902e-02 4.658959396388796e-15 + 1.000000000000000e+00 5.158863779039475e-02 2.496311679602705e-15 + 1.202264434617413e+00 4.913983755302447e-02 2.503975647353570e-15 + 1.445439770745928e+00 4.675806345070745e-02 1.980624000103322e-15 + 1.737800828749376e+00 4.444721590565470e-02 3.513326611439523e-15 + 2.089296130854041e+00 4.221024763556332e-02 2.128775949903540e-15 + 2.511886431509582e+00 4.004928271457441e-02 2.084732824400213e-15 + 3.019951720402019e+00 3.796572391712868e-02 2.057863428784457e-15 + 3.630780547701010e+00 3.596034888344765e-02 2.149696722374579e-15 + 4.365158322401657e+00 3.403339584700401e-02 2.506590750983091e-15 + 5.248074602497723e+00 3.218463976982702e-02 2.666959749115830e-15 + 6.309573444801930e+00 3.041345976812730e-02 1.843390243429058e-15 + 7.585775750291836e+00 2.871889869982439e-02 2.075866723337706e-15 + 9.120108393559097e+00 2.709971574419922e-02 2.614004879642500e-15 + 1.096478196143185e+01 2.555443274573189e-02 2.784239762991527e-15 + 1.318256738556407e+01 2.408137502873176e-02 4.417788851818592e-15 + 1.584893192461114e+01 2.267870732135474e-02 2.346418536174242e-15 + 1.905460717963248e+01 2.134446535879641e-02 3.159630166116848e-15 + 2.290867652767775e+01 2.007658366786368e-02 3.067450163255898e-15 + 2.754228703338169e+01 1.887291997221849e-02 4.085090221270331e-15 + 3.311311214825908e+01 1.773127660229970e-02 4.662766446257259e-15 + 3.981071705534969e+01 1.664941924664940e-02 5.219648685301088e-15 + 4.786300923226381e+01 1.562509334029200e-02 5.188731853763820e-15 + 5.754399373371567e+01 1.465603834912039e-02 5.298056449394350e-15 + 6.918309709189363e+01 1.374000017615125e-02 6.088475789849585e-15 + 8.317637711026708e+01 1.287474188620420e-02 5.607884807044724e-15 diff --git a/figs/condensate.fig/condensate.gnuplot b/figs/condensate.fig/condensate.gnuplot new file mode 100644 index 0000000..f1c689d --- /dev/null +++ b/figs/condensate.fig/condensate.gnuplot @@ -0,0 +1,36 @@ +set ylabel "$\\eta$" norotate +set xlabel "$\\rho$" + +set yrange [0.9:1] +set ytics 0.91, 0.03 +set mytics 3 + +set xrange [1e-6:100] +set xtics 1e-6, 100, 100 +set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100) +unset mxtics + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +set key off + +# set linestyle +set style line 1 linetype rgbcolor "#4169E1" linewidth 2 +set style line 2 linetype rgbcolor "#DC143C" linewidth 2 +set style line 3 linetype rgbcolor "#32CD32" linewidth 2 +set style line 4 linetype rgbcolor "#4B0082" linewidth 2 +set style line 5 linetype rgbcolor "#DAA520" linewidth 2 + +set pointsize 0.6 + +set label at 0.000005,0.91 "Bogolyubov" textcolor "#32CD32" + +set logscale x + +a=1.25435641059 + +plot "simpleq.dat" u 1:(1-$2) w l ls 1, \ + "bigeq.dat" u 1:(1-$2) w l ls 4 , \ + 1-8/(3*sqrt(pi))*sqrt(x*a**3) linestyle 3 dashtype "." ,\ + "holzmann_2019-12-25.dat" u 1:(1-$3) ls 2 diff --git a/figs/condensate.fig/holzmann_2019-12-25.dat b/figs/condensate.fig/holzmann_2019-12-25.dat new file mode 100644 index 0000000..96689cb --- /dev/null +++ b/figs/condensate.fig/holzmann_2019-12-25.dat @@ -0,0 +1,11 @@ +## data from M. Holzmann, 2019-09-22 +# rho E0 n0 +1e-6 7.902e-6 +1e-4 8.3441e-4 0.0171 +1e-3 9.13384e-3 0.0481 +1e-2 1.061073e-1 0.0871 +1e-1 1.19182e+0 0.0851 +1e-0 1.24302e+1 0.0587 +1e+1 1.25442e+2 0.0319 +5e+1 6.28032e+2 0.021 + diff --git a/figs/condensate.fig/simpleq.dat b/figs/condensate.fig/simpleq.dat new file mode 100644 index 0000000..348121c --- /dev/null +++ b/figs/condensate.fig/simpleq.dat @@ -0,0 +1,100 @@ + 1.000000000000000e-06 2.095081711925015e-03 + 1.202264434617413e-06 2.295235280091131e-03 + 1.445439770745928e-06 2.514296186738034e-03 + 1.737800828749376e-06 2.754005992218143e-03 + 2.089296130854041e-06 3.016257261240048e-03 + 2.511886431509582e-06 3.303104592145314e-03 + 3.019951720402019e-06 3.616775975726918e-03 + 3.630780547701017e-06 3.959684344305409e-03 + 4.365158322401657e-06 4.334439155646415e-03 + 5.248074602497723e-06 4.743857767750661e-03 + 6.309573444801930e-06 5.190976310677877e-03 + 7.585775750291836e-06 5.679059686385030e-03 + 9.120108393559096e-06 6.211610171947045e-03 + 1.096478196143185e-05 6.792374027485015e-03 + 1.318256738556407e-05 7.425345312781278e-03 + 1.584893192461114e-05 8.114765932045185e-03 + 1.905460717963248e-05 8.865120699464721e-03 + 2.290867652767775e-05 9.681125931789915e-03 + 2.754228703338163e-05 1.056770975064344e-02 + 3.311311214825908e-05 1.152998189333092e-02 + 3.981071705534969e-05 1.257319039145271e-02 + 4.786300923226380e-05 1.370266197723624e-02 + 5.754399373371566e-05 1.492372253381352e-02 + 6.918309709189363e-05 1.624159332185176e-02 + 8.317637711026709e-05 1.766125812610249e-02 + 1.000000000000000e-04 1.918729591875359e-02 + 1.202264434617413e-04 2.082367319967555e-02 + 1.445439770745928e-04 2.257348995912804e-02 + 1.737800828749376e-04 2.443867336254203e-02 + 2.089296130854039e-04 2.641961398528058e-02 + 2.511886431509580e-04 2.851474099050601e-02 + 3.019951720402016e-04 3.072003537104471e-02 + 3.630780547701014e-04 3.302848464372067e-02 + 4.365158322401661e-04 3.542948859291789e-02 + 5.248074602497728e-04 3.790823417663501e-02 + 6.309573444801930e-04 4.044506877087432e-02 + 7.585775750291835e-04 4.301491450154334e-02 + 9.120108393559096e-04 4.558678199565728e-02 + 1.096478196143185e-03 4.812345827946150e-02 + 1.318256738556408e-03 5.058145864328128e-02 + 1.584893192461114e-03 5.291134289200051e-02 + 1.905460717963246e-03 5.505849827399160e-02 + 2.290867652767772e-03 5.696447960043553e-02 + 2.754228703338166e-03 5.856896678930269e-02 + 3.311311214825911e-03 5.981234782238041e-02 + 3.981071705534973e-03 6.063886048364867e-02 + 4.786300923226385e-03 6.100013371714988e-02 + 5.754399373371567e-03 6.085886970213172e-02 + 6.918309709189363e-03 6.019231791545348e-02 + 8.317637711026709e-03 5.899513433487237e-02 + 1.000000000000000e-02 5.728121486315967e-02 + 1.202264434617413e-02 5.508415858187780e-02 + 1.445439770745928e-02 5.245615721904299e-02 + 1.737800828749376e-02 4.946530746709376e-02 + 2.089296130854041e-02 4.619156855992348e-02 + 2.511886431509582e-02 4.272179185226004e-02 + 3.019951720402019e-02 3.914438480508303e-02 + 3.630780547701010e-02 3.554420649152192e-02 + 4.365158322401656e-02 3.199821953636445e-02 + 5.248074602497723e-02 2.857226663349834e-02 + 6.309573444801930e-02 2.531914059520501e-02 + 7.585775750291836e-02 2.227792229852985e-02 + 9.120108393559097e-02 1.947440831436047e-02 + 1.096478196143185e-01 1.692235880228233e-02 + 1.318256738556407e-01 1.462526717442258e-02 + 1.584893192461114e-01 1.257837345877809e-02 + 1.905460717963248e-01 1.077069465848733e-02 + 2.290867652767775e-01 9.186909564013418e-03 + 2.754228703338169e-01 7.808998508205012e-03 + 3.311311214825908e-01 6.617591964706389e-03 + 3.981071705534969e-01 5.593022042416338e-03 + 4.786300923226380e-01 4.716097668760250e-03 + 5.754399373371566e-01 3.968639441621027e-03 + 6.918309709189363e-01 3.333816454742892e-03 + 8.317637711026709e-01 2.796327604398189e-03 + 1.000000000000000e+00 2.342466331442259e-03 + 1.202264434617413e+00 1.960102269258443e-03 + 1.445439770745928e+00 1.638607138480099e-03 + 1.737800828749376e+00 1.368746272215081e-03 + 2.089296130854041e+00 1.142551829784601e-03 + 2.511886431509582e+00 9.531892670181336e-04 + 3.019951720402019e+00 7.948250154423670e-04 + 3.630780547701010e+00 6.625005224425910e-04 + 4.365158322401657e+00 5.520157121243856e-04 + 5.248074602497723e+00 4.598234179345307e-04 + 6.309573444801930e+00 3.829352915009887e-04 + 7.585775750291836e+00 3.188389988971121e-04 + 9.120108393559097e+00 2.654260840747906e-04 + 1.096478196143185e+01 2.209296357978901e-04 + 1.318256738556407e+01 1.838707817059403e-04 + 1.584893192461114e+01 1.530130079086820e-04 + 1.905460717963248e+01 1.273233330370514e-04 + 2.290867652767775e+01 1.059394293104648e-04 + 2.754228703338169e+01 8.814186420712528e-05 + 3.311311214825908e+01 7.333072418003886e-05 + 3.981071705534969e+01 6.100596972384632e-05 + 4.786300923226381e+01 5.075095479639026e-05 + 5.754399373371567e+01 4.221862079919067e-05 + 6.918309709189363e+01 3.511994492291246e-05 + 8.317637711026708e+01 2.921428437169262e-05 diff --git a/figs/condensate16.fig/.energy16.gnuplot.swp b/figs/condensate16.fig/.energy16.gnuplot.swp Binary files differnew file mode 100644 index 0000000..d23db08 --- /dev/null +++ b/figs/condensate16.fig/.energy16.gnuplot.swp diff --git a/figs/condensate16.fig/2020-05-22+16.dat b/figs/condensate16.fig/2020-05-22+16.dat new file mode 100644 index 0000000..c28285d --- /dev/null +++ b/figs/condensate16.fig/2020-05-22+16.dat @@ -0,0 +1,7 @@ +# rho E0 n0 + 1e-3 0.05195 0.61 + 5e-3 0.449 0.40 + 1e-2 1.1335 0.34 + 2e-2 2.748 0.33 + 1e-1 17.797 0.43 + 1e+0 197.35 0.70 diff --git a/figs/condensate16.fig/Makefile b/figs/condensate16.fig/Makefile new file mode 100644 index 0000000..d44f73c --- /dev/null +++ b/figs/condensate16.fig/Makefile @@ -0,0 +1,35 @@ +PROJECTNAME=condensate16 + +SIMPLEQ=~/Work/Research/2018+bose_gas/cmp/simpleq + +DATS=simpleq16.dat medeq16.dat +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) +TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME)) + +all: $(PDFS) + +$(PDFS): $(DATS) + gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@) + pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@) + +simpleq16.dat: + julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=16" -M simpleq condensate_fraction > $@ +medeq16.dat: + julia -p 8 $(SIMPLEQ)/main.jl -p "aK=1;aL1=1;aL2=1;aL3=0;bK=1;bL1=1;bL2=1;gK=1;gL2=1;gL3=0;N=12;P=8;v_a=16" -M medeq condensate_fraction > $@ + + +install: $(PDFS) + cp $^ $(INSTALLDIR)/ + +clean-aux: + rm -f $(addsuffix .tikz.tex, $(PROJECTNAME)) + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + +clean-dat: + rm -f $(DATS) + +clean-tex: + rm -f $(PDFS) + +clean: clean-aux clean-tex diff --git a/figs/condensate16.fig/condensate16.gnuplot b/figs/condensate16.fig/condensate16.gnuplot new file mode 100644 index 0000000..e94eb1a --- /dev/null +++ b/figs/condensate16.fig/condensate16.gnuplot @@ -0,0 +1,34 @@ +set ylabel "$\\eta$" norotate offset -1,0 +set xlabel "$\\rho$" + +set xtics 1e-6, 100, 100 +set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100) +unset mxtics + +#set ytics 0.6, 0.1 +set mytics 2 + +set xrange [0.000001:100] + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +set key off + + +# set linestyle +set style line 1 linetype rgbcolor "#4169E1" linewidth 2 +set style line 2 linetype rgbcolor "#DC143C" linewidth 2 +set style line 3 linetype rgbcolor "#32CD32" linewidth 2 +set style line 4 linetype rgbcolor "#4B0082" linewidth 2 +set style line 5 linetype rgbcolor "#DAA520" linewidth 2 + +set pointsize 1 + +set logscale x + +plot \ + "simpleq16.dat" using 1:($3<1e-5 ? 1-$2 : 1/0) with lines ls 1 ,\ + "medeq16.dat" using 1:($3<1e-5 ? 1-$2 : 1/0) with lines ls 4 ,\ + "2020-05-22+16.dat" using 1:3 with points ls 2 + diff --git a/figs/condensate16.fig/medeq16.dat b/figs/condensate16.fig/medeq16.dat new file mode 100644 index 0000000..16ef72d --- /dev/null +++ b/figs/condensate16.fig/medeq16.dat @@ -0,0 +1,100 @@ + 1.000000000000000e-06 1.166000749536307e-02 1.397500557749096e-14 + 1.202264434617413e-06 1.294150659557208e-02 1.638378932477403e-14 + 1.445439770745928e-06 1.433395863576837e-02 2.068669778175053e-14 + 1.737800828749376e-06 1.585523520080719e-02 9.413457244472722e-15 + 2.089296130854041e-06 1.752468227078358e-02 2.147730951610164e-14 + 2.511886431509582e-06 1.936219857512355e-02 5.079185685242370e-14 + 3.019951720402019e-06 2.138821025238190e-02 4.890613903920614e-14 + 3.630780547701017e-06 2.362406333962305e-02 3.239855276438957e-14 + 4.365158322401657e-06 2.609258293662487e-02 6.114316674680731e-14 + 5.248074602497723e-06 2.881866901219256e-02 2.406593746021106e-14 + 6.309573444801930e-06 3.182986273284136e-02 5.235506117228457e-14 + 7.585775750291836e-06 3.515686411604940e-02 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2.773788643238822e-15 + 6.309573444801930e+00 3.849693047135169e-04 5.605531588703275e-14 + 7.585775750291836e+00 3.202498832578166e-04 1.548482473273102e-15 + 9.120108393559097e+00 2.664043442730844e-04 5.542616472939282e-15 + 1.096478196143185e+01 2.216076961608340e-04 5.416841008960720e-15 + 1.318256738556407e+01 1.843406276770280e-04 1.051948766670258e-13 + 1.584893192461114e+01 1.533384958473269e-04 3.020416191025176e-15 + 1.905460717963248e+01 1.275487688416503e-04 1.054514720940622e-13 + 2.290867652767775e+01 1.060955403032162e-04 1.054818735884649e-13 + 2.754228703338169e+01 8.824995249206293e-05 1.068333765010024e-13 + 3.311311214825908e+01 7.340555293075552e-05 5.311424682002792e-14 + 3.981071705534969e+01 6.105776757545735e-05 8.573716686070972e-15 + 4.786300923226381e+01 5.078680698963938e-05 5.255692893479381e-14 + 5.754399373371567e+01 4.224343422123316e-05 5.412915990778012e-16 + 6.918309709189363e+01 3.513711727611226e-05 5.629397185139020e-14 + 8.317637711026708e+01 2.922616801548849e-05 8.852629630882290e-12 diff --git a/figs/energy.fig/Makefile b/figs/energy.fig/Makefile new file mode 100644 index 0000000..e8d3f12 --- /dev/null +++ b/figs/energy.fig/Makefile @@ -0,0 +1,28 @@ +PROJECTNAME=erho_effective erho_fulleq erho_lowhigh + +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) + +all: $(PDFS) + +$(PDFS): + gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tex, $@) + pdflatex -file-line-error $(patsubst %.pdf, %.tex, $@) + +install: $(PDFS) + cp $^ $(INSTALLDIR)/ + +$(LIBS): + ln -fs libs/$@ ./ + +clean-libs: + rm -f $(LIBS) + +clean-aux: + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + rm -f $(addsuffix .tex, $(PROJECTNAME)) + +clean-tex: + rm -f $(PDFS) + +clean: clean-libs clean-aux clean-tex diff --git a/figs/energy.fig/erho.dat b/figs/energy.fig/erho.dat new file mode 100644 index 0000000..837439f --- /dev/null +++ b/figs/energy.fig/erho.dat @@ -0,0 +1,104 @@ + # v(x)=exp(-|x|), order=100, tolerance=1e-14 + # + # rho energy + # + 1.00000000e-06 7.93445832e-06 + 1.20226443e-06 9.54545091e-06 + 1.44543977e-06 1.14842358e-05 + 1.73780083e-06 1.38177301e-05 + 2.08929613e-06 1.66265809e-05 + 2.51188643e-06 2.00080034e-05 + 3.01995172e-06 2.40792133e-05 + 3.63078055e-06 2.89815779e-05 + 4.36515832e-06 3.48856405e-05 + 5.24807460e-06 4.19972045e-05 + 6.30957344e-06 5.05647046e-05 + 7.58577575e-06 6.08881446e-05 + 9.12010839e-06 7.33299394e-05 + 1.09647820e-05 8.83280780e-05 + 1.31825674e-05 1.06412115e-04 + 1.58489319e-05 1.28222614e-04 + 1.90546072e-05 1.54534805e-04 + 2.29086765e-05 1.86287394e-04 + 2.75422870e-05 2.24617677e-04 + 3.31131121e-05 2.70904370e-04 + 3.98107171e-05 3.26819905e-04 + 4.78630092e-05 3.94394317e-04 + 5.75439937e-05 4.76093386e-04 + 6.91830971e-05 5.74914264e-04 + 8.31763771e-05 6.94502595e-04 + 1.00000000e-04 8.39296065e-04 + 1.20226443e-04 1.01470042e-03 + 1.44543977e-04 1.22730542e-03 + 1.73780083e-04 1.48514988e-03 + 2.08929613e-04 1.79804690e-03 + 2.51188643e-04 2.17798310e-03 + 3.01995172e-04 2.63960836e-03 + 3.63078055e-04 3.20083623e-03 + 4.36515832e-04 3.88357954e-03 + 5.24807460e-04 4.71465030e-03 + 6.30957344e-04 5.72685888e-03 + 7.58577575e-04 6.96035420e-03 + 9.12010839e-04 8.46425370e-03 + 1.09647820e-03 1.02986208e-02 + 1.31825674e-03 1.25368572e-02 + 1.58489319e-03 1.52685874e-02 + 1.90546072e-03 1.86031268e-02 + 2.29086765e-03 2.26736380e-02 + 2.75422870e-03 2.76420977e-02 + 3.31131121e-03 3.37052167e-02 + 3.98107171e-03 4.11014850e-02 + 4.78630092e-03 5.01195435e-02 + 5.75439937e-03 6.11081308e-02 + 6.91830971e-03 7.44879092e-02 + 8.31763771e-03 9.07655413e-02 + 1.00000000e-02 1.10550483e-01 + 1.20226443e-02 1.34575061e-01 + 1.44543977e-02 1.63718539e-01 + 1.73780083e-02 1.99036030e-01 + 2.08929613e-02 2.41793284e-01 + 2.51188643e-02 2.93508614e-01 + 3.01995172e-02 3.56003446e-01 + 3.63078055e-02 4.31463277e-01 + 4.36515832e-02 5.22511186e-01 + 5.24807460e-02 6.32296416e-01 + 6.30957344e-02 7.64601077e-01 + 7.58577575e-02 9.23968602e-01 + 9.12010839e-02 1.11585830e+00 + 1.09647820e-01 1.34683126e+00 + 1.31825674e-01 1.62477387e+00 + 1.58489319e-01 1.95916654e+00 + 1.90546072e-01 2.36140673e+00 + 2.29086765e-01 2.84519724e+00 + 2.75422870e-01 3.42701297e+00 + 3.31131121e-01 4.12666196e+00 + 3.98107171e-01 4.96795983e+00 + 4.78630092e-01 5.97954056e+00 + 5.75439937e-01 7.19583118e+00 + 6.91830971e-01 8.65822353e+00 + 8.31763771e-01 1.04164830e+01 + 1.00000000e+00 1.25304420e+01 + 1.20226443e+00 1.50720365e+01 + 1.44543977e+00 1.81277534e+01 + 1.73780083e+00 2.18015742e+01 + 2.08929613e+00 2.62185132e+01 + 2.51188643e+00 3.15288712e+01 + 3.01995172e+00 3.79133506e+01 + 3.63078055e+00 4.55892039e+01 + 4.36515832e+00 5.48176270e+01 + 5.24807460e+00 6.59126465e+01 + 6.30957344e+00 7.92518063e+01 + 7.58577575e+00 9.52890139e+01 + 9.12010839e+00 1.14569987e+02 + 1.09647820e+01 1.37750822e+02 + 1.31825674e+01 1.65620322e+02 + 1.58489319e+01 1.99126836e+02 + 1.90546072e+01 2.39410530e+02 + 2.29086765e+01 2.87842186e+02 + 2.75422870e+01 3.46069846e+02 + 3.31131121e+01 4.16074894e+02 + 3.98107171e+01 5.00239474e+02 + 4.78630092e+01 6.01427558e+02 + 5.75439937e+01 7.23082394e+02 + 6.91830971e+01 8.69343678e+02 + 8.31763771e+01 1.04518842e+03 diff --git a/figs/energy.fig/erho_effective.gnuplot b/figs/energy.fig/erho_effective.gnuplot new file mode 100644 index 0000000..f26252e --- /dev/null +++ b/figs/energy.fig/erho_effective.gnuplot @@ -0,0 +1,38 @@ +set ylabel "$\\displaystyle\\frac{e}{\\rho}$" norotate offset -1,0 +set xlabel "$\\rho$" + +set xtics 1e-6, 100, 100 +set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100) +unset mxtics + +set ytics 8,1 +set mytics 2 + +set xrange [0.000001:100] +set yrange [7.5:13.5] + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +set key off + + +# set linestyle +set style line 1 linetype rgbcolor "#4169E1" linewidth 3 +set style line 2 linetype rgbcolor "#DC143C" linewidth 3 +set style line 3 linetype rgbcolor "#32CD32" linewidth 3 +set style line 4 linetype rgbcolor "#4B0082" linewidth 3 +set style line 5 linetype rgbcolor "#DAA520" linewidth 3 + +set pointsize 1 + +set logscale x + +a=1.25435641059 + +set label at 0.0001,2*pi*a*1.03 "LHY" textcolor "#DAA520" +set label at 0.1,4.1*pi "Hartree" textcolor "#32CD32" + +plot "erho.dat" using 1:($2/$1) with lines linestyle 1 ,\ + 2*pi*a*(1+128/15/sqrt(pi)*sqrt(x*a**3)) linestyle 5 dashtype "." ,\ + 4*pi linestyle 3 dashtype "." diff --git a/figs/energy.fig/erho_fulleq.dat b/figs/energy.fig/erho_fulleq.dat new file mode 100644 index 0000000..351d1b9 --- /dev/null +++ b/figs/energy.fig/erho_fulleq.dat @@ -0,0 +1,100 @@ + 1.000000000000000e-06 7.943042518656766e-06 0 + 1.202264434617413e-06 9.550219866068997e-06 0 + 1.445439770745928e-06 1.148608224097378e-05 1 + 1.737800828749376e-06 1.381647407426905e-05 1 + 2.089296130854041e-06 1.662160583174429e-05 0 + 2.511886431509582e-06 2.000065135391551e-05 0 + 3.019951720402019e-06 2.406839054942614e-05 0 + 3.630780547701017e-06 2.896662133595565e-05 1 + 4.365158322401657e-06 3.486570260772683e-05 1 + 5.248074602497723e-06 4.197087478032896e-05 1 + 6.309573444801930e-06 5.052956242205629e-05 1 + 7.585775750291836e-06 6.084048678334965e-05 1 + 9.120108393559096e-06 7.326450648917462e-05 1 + 1.096478196143185e-05 8.823760552067889e-05 1 + 1.318256738556407e-05 1.062866339996179e-04 1 + 1.584893192461114e-05 1.280484412743087e-04 1 + 1.905460717963248e-05 1.542931396948374e-04 1 + 2.290867652767775e-05 1.859523935537466e-04 1 + 2.754228703338163e-05 2.241538298379074e-04 1 + 3.311311214825908e-05 2.702629184292266e-04 1 + 3.981071705534969e-05 3.259339774051344e-04 1 + 4.786300923226380e-05 3.931723354869787e-04 1 + 5.754399373371566e-05 4.744101435386617e-04 1 + 6.918309709189363e-05 5.725988899895806e-04 1 + 8.317637711026709e-05 6.913223659756494e-04 1 + 1.000000000000000e-04 8.349346745163116e-04 1 + 1.202264434617413e-04 1.008728918608530e-03 1 + 1.445439770745928e-04 1.219143475424315e-03 1 + 1.737800828749376e-04 1.474014314386416e-03 1 + 2.089296130854039e-04 1.782883700975914e-03 1 + 2.511886431509580e-04 2.157377911005317e-03 1 + 3.019951720402016e-04 2.611669336976909e-03 1 + 3.630780547701014e-04 3.163041683927843e-03 1 + 4.365158322401661e-04 3.832580921405091e-03 1 + 5.248074602497728e-04 4.646019387820095e-03 1 + 6.309573444801930e-04 5.634766055532872e-03 1 + 7.585775750291835e-04 6.837162598523666e-03 1 + 9.120108393559096e-04 8.300012713479526e-03 1 + 1.096478196143185e-03 1.008044129788173e-02 1 + 1.318256738556408e-03 1.224815077758103e-02 1 + 1.584893192461114e-03 1.488815434797412e-02 1 + 1.905460717963246e-03 1.810408049926405e-02 1 + 2.290867652767772e-03 2.202216044849479e-02 1 + 2.754228703338166e-03 2.679603069994577e-02 1 + 3.311311214825911e-03 3.261250778551406e-02 1 + 3.981071705534973e-03 3.969852233927642e-02 1 + 4.786300923226385e-03 4.832943621884326e-02 1 + 5.754399373371567e-03 5.883901075761193e-02 1 + 6.918309709189363e-03 7.163134806415740e-02 1 + 8.317637711026709e-03 8.719519272244317e-02 1 + 1.000000000000000e-02 1.061210611088454e-01 1 + 1.202264434617413e-02 1.291217632376783e-01 1 + 1.445439770745928e-02 1.570570011615084e-01 1 + 1.737800828749376e-02 1.909628719282619e-01 1 + 2.089296130854041e-02 2.320872756251715e-01 1 + 2.511886431509582e-02 2.819324351385837e-01 1 + 3.019951720402019e-02 3.423059810454135e-01 1 + 3.630780547701010e-02 4.153823512868898e-01 1 + 4.365158322401656e-02 5.037766102499891e-01 1 + 5.248074602497723e-02 6.106332154610473e-01 1 + 6.309573444801930e-02 7.397327648968161e-01 1 + 7.585775750291836e-02 8.956203622431048e-01 1 + 9.120108393559097e-02 1.083759966304908e+00 1 + 1.096478196143185e-01 1.310719973979596e+00 1 + 1.318256738556407e-01 1.584396355238566e+00 1 + 1.584893192461114e-01 1.914280945866737e+00 1 + 1.905460717963248e-01 2.311784046064119e+00 1 + 2.290867652767775e-01 2.790622317703228e+00 1 + 2.754228703338169e-01 3.367285183378040e+00 1 + 3.311311214825908e-01 4.061595587917465e+00 1 + 3.981071705534969e-01 4.897384186423424e+00 1 + 4.786300923226380e-01 5.903299886083452e+00 1 + 5.754399373371566e-01 7.113784322007290e+00 1 + 6.918309709189363e-01 8.570243441380599e+00 1 + 8.317637711026709e-01 1.032245608693097e+01 1 + 1.000000000000000e+00 1.243026753303222e+01 1 + 1.202264434617413e+00 1.496562561057760e+01 1 + 1.445439770745928e+00 1.801502869576436e+01 1 + 1.737800828749376e+00 2.168246883802093e+01 1 + 2.089296130854041e+00 2.609297014699965e+01 1 + 2.511886431509582e+00 3.139684282320142e+01 1 + 3.019951720402019e+00 3.777479758723231e+01 1 + 3.630780547701010e+00 4.544409456028400e+01 1 + 4.365158322401657e+00 5.466593586138625e+01 1 + 5.248074602497723e+00 6.575435350738108e+01 1 + 6.309573444801930e+00 7.908689506783082e+01 1 + 7.585775750291836e+00 9.511747067219883e+01 1 + 9.120108393559097e+00 1.143917984731058e+02 1 + 1.096478196143185e+01 1.375659740282897e+02 1 + 1.318256738556407e+01 1.654287952107530e+02 1 + 1.584893192461114e+01 1.989286012247062e+02 1 + 1.905460717963248e+01 2.392055363411829e+02 0 + 2.290867652767775e+01 2.876303621855438e+02 0 + 2.754228703338169e+01 3.458511552270688e+02 0 + 3.311311214825908e+01 4.158492765508882e+02 0 + 3.981071705534969e+01 5.000067330413117e+02 0 + 4.786300923226381e+01 6.011878314695363e+02 0 + 5.754399373371567e+01 7.228352310513908e+02 0 + 6.918309709189363e+01 8.690894472935229e+02 0 + 8.317637711026708e+01 1.044926046890143e+03 0 diff --git a/figs/energy.fig/erho_fulleq.gnuplot b/figs/energy.fig/erho_fulleq.gnuplot new file mode 100644 index 0000000..2927ead --- /dev/null +++ b/figs/energy.fig/erho_fulleq.gnuplot @@ -0,0 +1,37 @@ +set ylabel "$\\displaystyle\\frac{e}{\\rho}$" norotate offset -1,0 +set xlabel "$\\rho$" + +set xtics 1e-6, 100, 100 +set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100) +unset mxtics + +set ytics 8,1 +set mytics 2 + +set xrange [0.000001:100] +set yrange [7.5:13.5] + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +set key off + + +# set linestyle +set style line 1 linetype rgbcolor "#4169E1" linewidth 3 +set style line 2 linetype rgbcolor "#DC143C" linewidth 3 +set style line 3 linetype rgbcolor "#32CD32" linewidth 3 +set style line 4 linetype rgbcolor "#4B0082" linewidth 3 +set style line 5 linetype rgbcolor "#DAA520" linewidth 3 + +set pointsize 1 + +set logscale x + +a=1.25435641059 + +plot "erho.dat" using 1:($2/$1) with lines linestyle 1 ,\ + "erho_fulleq.dat" using 1:($2/$1) with lines linestyle 4 ,\ + 2*pi*a*(1+128/15/sqrt(pi)*sqrt(x*a**3)) linestyle 5 dashtype "." ,\ + 4*pi linestyle 3 dashtype "." ,\ + "holzmann_2019-12-25.dat" using 1:($2/$1) with points linestyle 2 diff --git a/figs/energy.fig/erho_lowhigh.gnuplot b/figs/energy.fig/erho_lowhigh.gnuplot new file mode 100644 index 0000000..9d2a590 --- /dev/null +++ b/figs/energy.fig/erho_lowhigh.gnuplot @@ -0,0 +1,37 @@ +set ylabel "$\\displaystyle\\frac{e}{\\rho}$" norotate offset -1,0 +set xlabel "$\\rho$" + +set xtics 1e-6, 100, 100 +set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100) +unset mxtics + +set ytics 8,1 +set mytics 2 + +set xrange [0.000001:100] +set yrange [7.5:13.5] + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +set key off + + +# set linestyle +set style line 1 linetype rgbcolor "#4169E1" linewidth 3 +set style line 2 linetype rgbcolor "#DC143C" linewidth 3 +set style line 3 linetype rgbcolor "#32CD32" linewidth 3 +set style line 4 linetype rgbcolor "#4B0082" linewidth 3 +set style line 5 linetype rgbcolor "#DAA520" linewidth 3 + +set pointsize 1 + +set logscale x + +a=1.25435641059 + +set label at 0.0001,2*pi*a*1.03 "LHY" textcolor "#DAA520" +set label at 0.1,4.1*pi "Hartree" textcolor "#32CD32" + +plot 2*pi*a*(1+128/15/sqrt(pi)*sqrt(x*a**3)) linestyle 5 dashtype "." ,\ + 4*pi linestyle 3 dashtype "." diff --git a/figs/energy.fig/holzmann_2019-12-25.dat b/figs/energy.fig/holzmann_2019-12-25.dat new file mode 100644 index 0000000..96689cb --- /dev/null +++ b/figs/energy.fig/holzmann_2019-12-25.dat @@ -0,0 +1,11 @@ +## data from M. Holzmann, 2019-09-22 +# rho E0 n0 +1e-6 7.902e-6 +1e-4 8.3441e-4 0.0171 +1e-3 9.13384e-3 0.0481 +1e-2 1.061073e-1 0.0871 +1e-1 1.19182e+0 0.0851 +1e-0 1.24302e+1 0.0587 +1e+1 1.25442e+2 0.0319 +5e+1 6.28032e+2 0.021 + diff --git a/figs/energy16.fig/2020-05-22+16.dat b/figs/energy16.fig/2020-05-22+16.dat new file mode 100644 index 0000000..c28285d --- /dev/null +++ b/figs/energy16.fig/2020-05-22+16.dat @@ -0,0 +1,7 @@ +# rho E0 n0 + 1e-3 0.05195 0.61 + 5e-3 0.449 0.40 + 1e-2 1.1335 0.34 + 2e-2 2.748 0.33 + 1e-1 17.797 0.43 + 1e+0 197.35 0.70 diff --git a/figs/energy16.fig/Makefile b/figs/energy16.fig/Makefile new file mode 100644 index 0000000..964a8c5 --- /dev/null +++ b/figs/energy16.fig/Makefile @@ -0,0 +1,35 @@ +PROJECTNAME=energy16 + +SIMPLEQ=~/Work/Research/2018+bose_gas/cmp/simpleq + +DATS=simpleq16.dat medeq16.dat +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) +TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME)) + +all: $(PDFS) + +$(PDFS): $(DATS) + gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@) + pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@) + +simpleq16.dat: + julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=16" -M simpleq energy_rho > $@ +medeq16.dat: + julia -p 8 $(SIMPLEQ)/main.jl -p "aK=1;aL1=1;aL2=1;aL3=0;bK=1;bL1=1;bL2=1;gK=1;gL2=1;gL3=0;N=12;P=8;v_a=16" -M medeq energy_rho > $@ + + +install: $(PDFS) + cp $^ $(INSTALLDIR)/ + +clean-aux: + rm -f $(addsuffix .tikz.tex, $(PROJECTNAME)) + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + +clean-dat: + rm -f $(DATS) + +clean-tex: + rm -f $(PDFS) + +clean: clean-aux clean-tex diff --git a/figs/energy16.fig/energy16.gnuplot b/figs/energy16.fig/energy16.gnuplot new file mode 100644 index 0000000..dc996c5 --- /dev/null +++ b/figs/energy16.fig/energy16.gnuplot @@ -0,0 +1,34 @@ +set ylabel "$\\displaystyle\\frac{e}{\\rho}$" norotate offset -1,0 +set xlabel "$\\rho$" + +set xtics 1e-6, 100, 100 +set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100) +unset mxtics + +#set ytics 0.6, 0.1 +set mytics 2 + +set xrange [0.000001:100] + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +set key off + + +# set linestyle +set style line 1 linetype rgbcolor "#4169E1" linewidth 2 +set style line 2 linetype rgbcolor "#DC143C" linewidth 2 +set style line 3 linetype rgbcolor "#32CD32" linewidth 2 +set style line 4 linetype rgbcolor "#4B0082" linewidth 2 +set style line 5 linetype rgbcolor "#DAA520" linewidth 2 + +set pointsize 1 + +set logscale x + +plot \ + "simpleq16.dat" using 1:($3<1e-5 ? ($2/$1) : 1/0) with lines ls 1 ,\ + "medeq16.dat" using 1:($3<1e-5 ? ($2/$1) : 1/0) with lines ls 4 ,\ + "2020-05-22+16.dat" using 1:($2/$1) with points ls 2 + diff --git a/figs/energy16.fig/medeq16.dat b/figs/energy16.fig/medeq16.dat new file mode 100644 index 0000000..b670ef5 --- /dev/null +++ b/figs/energy16.fig/medeq16.dat @@ -0,0 +1,100 @@ + 1.000000000000000e-06 2.554068644475559e-05 1.397500557749096e-14 + 1.202264434617413e-06 3.080347047701689e-05 1.638378932477403e-14 + 1.445439770745928e-06 3.716098929256974e-05 2.068669778175053e-14 + 1.737800828749376e-06 4.484410409494435e-05 9.413457244472722e-15 + 2.089296130854041e-06 5.413333030032436e-05 2.147730951610164e-14 + 2.511886431509582e-06 6.536981275090576e-05 5.079185685242370e-14 + 3.019951720402019e-06 7.896881202049198e-05 4.890613903920614e-14 + 3.630780547701017e-06 9.543630295201912e-05 3.239855276438957e-14 + 4.365158322401657e-06 1.153894399986016e-04 6.114316674680731e-14 + 5.248074602497723e-06 1.395818383298505e-04 2.406593746021106e-14 + 6.309573444801930e-06 1.689348660488532e-04 5.235506117228457e-14 + 7.585775750291836e-06 2.045764562134621e-04 2.215175470514193e-14 + 9.120108393559096e-06 2.478893480268333e-04 1.629554526288622e-14 + 1.096478196143185e-05 3.005711817436355e-04 4.459384031826223e-15 + 1.318256738556407e-05 3.647095370618017e-04 7.959533672028488e-14 + 1.584893192461114e-05 4.428758660698791e-04 1.856627535995191e-14 + 1.905460717963248e-05 5.382433893959377e-04 1.690345207320381e-14 + 2.290867652767775e-05 6.547354778876219e-04 8.321647126329251e-15 + 2.754228703338163e-05 7.972129388261395e-04 1.217647346338456e-14 + 3.311311214825908e-05 9.717111086044649e-04 8.937613010647126e-15 + 3.981071705534969e-05 1.185740914212854e-03 1.053125999750607e-14 + 4.786300923226380e-05 1.448672358365188e-03 2.683673474487137e-14 + 5.754399373371566e-05 1.772224545950021e-03 1.137789331779729e-14 + 6.918309709189363e-05 2.171093851718767e-03 2.458170758492918e-14 + 8.317637711026709e-05 2.663761724994058e-03 3.251467169362365e-14 + 1.000000000000000e-04 3.273536719674966e-03 1.604790218801148e-14 + 1.202264434617413e-04 4.029902651256568e-03 1.208705427621754e-14 + 1.445439770745928e-04 4.970267643766135e-03 9.949882875987985e-15 + 1.737800828749376e-04 6.142238932807714e-03 9.175378143390922e-15 + 2.089296130854039e-04 7.606587760365588e-03 2.214874949422118e-14 + 2.511886431509580e-04 9.441120133796742e-03 8.309109937206045e-14 + 3.019951720402016e-04 1.174573571624843e-02 2.396263674278965e-13 + 3.630780547701014e-04 1.464904218848119e-02 7.677444642221211e-13 + 4.365158322401661e-04 1.831699983067385e-02 2.316125381119014e-12 + 5.248074602497728e-04 2.296420442581745e-02 6.550410386633497e-12 + 6.309573444801930e-04 2.886857870385148e-02 1.868355419086652e-15 + 7.585775750291835e-04 3.639043452656086e-02 2.423897582964416e-15 + 9.120108393559096e-04 4.599708799630445e-02 6.448772157311636e-15 + 1.096478196143185e-03 5.829445137902425e-02 5.163654832442502e-15 + 1.318256738556408e-03 7.406727707716829e-02 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1.390459431262479e+04 4.136504038005983e-15 + 8.317637711026708e+01 1.671803950512843e+04 4.852059592739983e-15 diff --git a/figs/energy16.fig/medeq4.dat b/figs/energy16.fig/medeq4.dat new file mode 100644 index 0000000..ffaa5eb --- /dev/null +++ b/figs/energy16.fig/medeq4.dat @@ -0,0 +1,100 @@ + 1.000000000000000e-06 1.627424240030753e-05 9.007835427072701e-12 + 1.202264434617413e-06 1.959943745344100e-05 1.671351637616213e-12 + 1.445439770745928e-06 2.360770720466136e-05 4.387069667322242e-12 + 1.737800828749376e-06 2.844048299127554e-05 3.371679780930921e-14 + 2.089296130854041e-06 3.426881796805706e-05 3.499980814968632e-14 + 2.511886431509582e-06 4.129969708194542e-05 7.218204810983588e-15 + 3.019951720402019e-06 4.978372244366768e-05 8.253688999006713e-15 + 3.630780547701017e-06 6.002448197752047e-05 1.233139066041191e-14 + 4.365158322401657e-06 7.238998092442059e-05 6.922441203895261e-15 + 5.248074602497723e-06 8.732660537970414e-05 2.847530345897527e-14 + 6.309573444801930e-06 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%.pdf, %.tikz.tex, $@) + pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@) + +bigeq2.dat: + for rho in 0.005 0.01 0.02 0.1 1; do \ + echo -n $$rho " " >> $@-tmp ;\ + julia $(SIMPLEQ)/main.jl -p "eq=bigeq;N=8;P=9;J=10;maxiter=100;v_a=2;rho=$$rho;minlrho=-6;nlrho=50" -M medeq energy >> $@-tmp ;\ + done + paste $@-tmp 2020-08-27+2.dat > $@ + rm $@-tmp +simpleq2.dat: + for lrho in -2.301029995 -2 -1.698970004 -1 0; do \ + julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=2;minlrho=$$lrho;nlrho=1" -M simpleq energy_rho >> $@-tmp ;\ + done + paste $@-tmp 2020-08-27+2.dat > $@ + rm $@-tmp + +install: $(PDFS) + cp $^ $(INSTALLDIR)/ + +clean-aux: + rm -f $(addsuffix .tikz.tex, $(PROJECTNAME)) + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + +clean-dat: + rm -f $(DATS) + +clean-tex: + rm -f $(PDFS) + +clean: clean-aux clean-tex diff --git a/figs/relative_energy.fig/bigeq2.dat b/figs/relative_energy.fig/bigeq2.dat new file mode 100644 index 0000000..d976640 --- /dev/null +++ b/figs/relative_energy.fig/bigeq2.dat @@ -0,0 +1,5 @@ +0.005 9.077274334771057e-02 4.210230174384609e-15 5e-3 0.09074 0.850 0.09086 0.851 +0.01 1.963333772412874e-01 5.103464326744255e-15 1e-2 0.19640 0.836 0.19657 0.84 +0.02 4.210128326609409e-01 4.686441858629907e-15 2e-2 0.4210 0.83 0.4214 0.83 +0.1 2.347849641433116e+00 1.470639915178939e-15 1e-1 2.3477 0.84 2.348 0.86 +1 2.481579120915402e+01 3.015163776163534e-15 1e+0 24.82 0.91 24.82 0.91 diff --git a/figs/relative_energy.fig/compare.gnuplot b/figs/relative_energy.fig/compare.gnuplot new file mode 100644 index 0000000..7461923 --- /dev/null +++ b/figs/relative_energy.fig/compare.gnuplot @@ -0,0 +1,31 @@ +set ylabel "energy relative error" +set xlabel "$\\rho$" + +set xtics 1e-6, 100, 100 +set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100) +unset mxtics + +set xrange [0.000001:100] + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +set key off + + +# set linestyle +set style line 1 linetype rgbcolor "#4169E1" linewidth 2 +set style line 2 linetype rgbcolor "#DC143C" linewidth 2 +set style line 3 linetype rgbcolor "#32CD32" linewidth 2 +set style line 4 linetype rgbcolor "#4B0082" linewidth 2 +set style line 5 linetype rgbcolor "#DAA520" linewidth 2 + +set pointsize 1 + +set logscale xy + +plot \ + "simpleq2.dat" using 1:($3<1e-5 ? abs($2-$5)/$5 : 1/0) with lp ls 1 ,\ + "bigeq2.dat" using 1:($3<1e-5 ? abs($2-$5)/$5 : 1/0) with lp ls 4 ,\ + "2020-08-27+2.dat" using 1:(abs($4-$2)/$2) with lp ls 2 + diff --git a/figs/relative_energy.fig/simpleq2.dat b/figs/relative_energy.fig/simpleq2.dat new file mode 100644 index 0000000..08240cd --- /dev/null +++ b/figs/relative_energy.fig/simpleq2.dat @@ -0,0 +1,5 @@ + 5.000000007644367e-03 9.849857484186206e-02 8.221496065916031e-13 5e-3 0.09074 0.850 0.09086 0.851 + 1.000000000000000e-02 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+TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME)) + +all: $(PDFS) + +$(PDFS): $(DATS) + gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@) + pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@) + +bigeq16-ux.dat: + julia $(SIMPLEQ)/main.jl -p "rho=2e-2;minlrho=-6;nlrho=60;v_a=16;eq=bigeq;N=12;P=8;xmax=10" -M medeq ux > $@ +simpleq16-ux.dat: + julia $(SIMPLEQ)/main.jl -p "rho=2e-2;minlrho=-6;nlrho=60;v_a=16;maxiter=100;xmax=10" -M simpleq ux > $@ + + +install: $(PDFS) + cp $^ $(INSTALLDIR)/ + +clean-aux: + rm -f $(addsuffix .tikz.tex, $(PROJECTNAME)) + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + +clean-dat: + rm -f $(DATS) + +clean-tex: + rm -f $(PDFS) + +clean: clean-aux clean-tex diff --git a/figs/ux.fig/bigeq16-ux.dat b/figs/ux.fig/bigeq16-ux.dat new file mode 100644 index 0000000..08eff9c --- /dev/null +++ b/figs/ux.fig/bigeq16-ux.dat @@ -0,0 +1,100 @@ + 1.000000000000000e-01 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8.600000000000000e+00 1.678855772852491e-03 + 8.699999999999999e+00 1.649618282520690e-03 + 8.800000000000001e+00 1.579446081146929e-03 + 8.900000000000000e+00 1.464374900812817e-03 + 9.000000000000000e+00 1.347291274957102e-03 + 9.100000000000000e+00 1.253368871316164e-03 + 9.199999999999999e+00 1.184600863339352e-03 + 9.300000000000001e+00 1.142766397549264e-03 + 9.400000000000000e+00 1.121137030434721e-03 + 9.500000000000000e+00 1.112504755685689e-03 + 9.600000000000000e+00 1.102561208594862e-03 + 9.699999999999999e+00 1.065200575964809e-03 + 9.800000000000001e+00 9.941123333848058e-04 + 9.900000000000000e+00 8.990416258250775e-04 + 1.000000000000000e+01 8.101378842737272e-04 diff --git a/figs/ux.fig/ux.gnuplot b/figs/ux.fig/ux.gnuplot new file mode 100644 index 0000000..a1da5e7 --- /dev/null +++ b/figs/ux.fig/ux.gnuplot @@ -0,0 +1,26 @@ +set ylabel "$u$" norotate offset -1,0 +set xlabel "$x$" + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +set key off + + +# set linestyle +set style line 1 linetype rgbcolor "#4169E1" linewidth 2 +set style line 2 linetype rgbcolor "#DC143C" linewidth 1 +set style line 3 linetype rgbcolor "#32CD32" linewidth 2 +set style line 4 linetype rgbcolor "#4B0082" linewidth 2 +set style line 5 linetype rgbcolor "#DAA520" linewidth 2 +set style line 6 linetype rgbcolor "#555500" linewidth 2 + +set pointsize 0.5 + +rho=1e-2 + +plot \ + "bigeq16-ux.dat" using 1:2 with lines ls 4 ,\ + "simpleq16-ux.dat" using 1:2 with lines ls 1 ,\ + "2020-07-02+ux-0.02.dat" using 1:(1-$2) ls 2 + diff --git a/libs/ian-presentation.cls b/libs/ian-presentation.cls new file mode 100644 index 0000000..91bd487 --- /dev/null +++ b/libs/ian-presentation.cls @@ -0,0 +1,187 @@ +%% +%% Ian's presentation class +%% + +%% TeX format +\NeedsTeXFormat{LaTeX2e}[1995/12/01] + +%% class name +\ProvidesClass{ian-presentation}[2017/09/29] + +\def\ian@defaultoptions{ + \pagestyle{plain} + \RequirePackage{color} + \RequirePackage{amssymb} +} + +%% paper dimensions +\setlength\paperheight{240pt} +\setlength\paperwidth{427pt} + +%% fonts +\input{size11.clo} +\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm} +\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf} +\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt} +\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf} +\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit} + +%% text dimensions +\textheight=208pt +\textwidth=370pt +\hoffset=-1in +\voffset=-1in +\oddsidemargin=24pt +\evensidemargin=24pt +\topmargin=8pt +\headheight=0pt +\headsep=0pt +\marginparsep=0pt +\marginparwidth=0pt +\footskip=16pt + + +%% remove default skips +\parindent=0pt +\parskip=0pt +\baselineskip=0pt + +%% something is wrong with \thepage, redefine it +\gdef\thepage{\the\c@page} + +%% correct vertical alignment at the end of a document +\AtEndDocument{ + % save total slide count + \immediate\write\@auxout{\noexpand\gdef\noexpand\slidecount{\thepage}} + \vfill + \eject +} + + +%% footer +\def\ps@plain{ + \def\@oddhead{} + \def\@evenhead{\@oddhead} + \def\@oddfoot{\tiny\hfill\thepage/\safe\slidecount\hfill} + \def\@evenfoot{\@oddfoot} +} +\def\ps@empty{ + \def\@oddhead{} + \def\@evenhead{\@oddhead} + \def\@oddfoot{} + \def\@evenfoot{\@oddfoot} +} + + +%% title of slide +\def\title#1{ + \hfil{\bf\large #1}\par + \hfil\vrule width0.75\textwidth height0.3pt\par + \vskip5pt +} + + +%% hyperlinks +% hyperlinkcounter +\newcounter{lncount} +% hyperref anchor +\def\hrefanchor{% +\stepcounter{lncount}% +\hypertarget{ln.\thelncount}{}% +} + +%% define a command and write it to aux file +\def\outdef#1#2{% + % define command% + \expandafter\xdef\csname #1\endcsname{#2}% + % hyperlink number% + \expandafter\xdef\csname #1@hl\endcsname{\thelncount}% + % write command to aux% + \immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1\endcsname{\csname #1\endcsname}}% + \immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1@hl\endcsname{\thelncount}}% +} + +%% can call commands even when they are not defined +\def\safe#1{% + \ifdefined#1% + #1% + \else% + {\color{red}\bf?}% + \fi% +} + + +%% itemize +\newlength\itemizeskip +% left margin for items +\setlength\itemizeskip{20pt} +\newlength\itemizeseparator +% space between the item symbol and the text +\setlength\itemizeseparator{5pt} +% penalty preceding an itemize +\def\itemizepenalty{0} +% counter counting the itemize level +\newcounter{itemizecount} + +% item symbol +\def\itemizept#1{ + \ifnum#1=1 + \textbullet + \else + $\scriptstyle\blacktriangleright$ + \fi +} + +\newlength\current@itemizeskip +\setlength\current@itemizeskip{0pt} +\def\itemize{ + \par\penalty\itemizepenalty\medskip\penalty\itemizepenalty + \addtocounter{itemizecount}{1} + \addtolength\current@itemizeskip{\itemizeskip} + \leftskip\current@itemizeskip +} +\def\enditemize{ + \addtocounter{itemizecount}{-1} + \addtolength\current@itemizeskip{-\itemizeskip} + \par\leftskip\current@itemizeskip + \medskip +} +\newlength\itempt@total +\def\item{ + \settowidth\itempt@total{\itemizept\theitemizecount} + \addtolength\itempt@total{\itemizeseparator} + \par + \medskip + \hskip-\itempt@total\itemizept\theitemizecount\hskip\itemizeseparator +} + +%% enumerate +\newcounter{enumerate@count} +\def\enumerate{ + \setcounter{enumerate@count}0 + \let\olditem\item + \let\olditemizept\itemizept + \def\item{ + % counter + \stepcounter{enumerate@count} + % set header + \def\itemizept{\theenumerate@count.} + % hyperref anchor + \hrefanchor + % define tag (for \label) + \xdef\tag{\theenumerate@count} + \olditem + } + \itemize +} +\def\endenumerate{ + \enditemize + \let\item\olditem + \let\itemizept\olditemizept +} + + +%% end +\ian@defaultoptions + +\endinput |